Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
An Efficient Primal-Dual Interior-Point Method for Minimizing a Sum of Euclidean Norms
SIAM Journal on Scientific Computing
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Electrocardiographic mapping (ECGM) is to estimate the cardiac activities from the measured body surface potentials (BSPs), in which the epicardial potentials (EPs) is often reconstructed. One of the challenges in ECGM problem is its ill-posedness, and regularization techniques are needed to obtain the clinically reasonable solutions. The total variation (TV) method has been validated in keeping the sharp edges and has found some preliminary applications in ECG inverse problem. In this study, we applied and compared two algorithms: lagged diffusivity (LD) fixed point iteration and primal dual-interior point method (PD-IPM), to implement TV regularization method in ECGM problem. With a realistic heart-lung-torso model, the TV methods are tested and compared to the L2-norm regularization methods in zero- and first-order. The simulation results demonstrate that the TV method can generate better EPs compared to the zero-order Tikhonov method. Compared to the first-order Tikhonov method, the TV's results are much sharper. For the two algorithms in TV method, the LD algorithm seems more robust than the PD-IPM in ECGM problem, though the PD-IPM converges faster.